scholarly journals Computing water flow through complex landscapes – Part 3: Fill–Spill–Merge: flow routing in depression hierarchies

2021 ◽  
Vol 9 (1) ◽  
pp. 105-121
Author(s):  
Richard Barnes ◽  
Kerry L. Callaghan ◽  
Andrew D. Wickert
Keyword(s):  
Data Structure ◽  
Water Conservation ◽  
Source Code ◽  
Planetary Science ◽  
Topographic Complexity ◽  
Flow Models ◽  
Detailed Explanation ◽  
Jacobi Iteration ◽  
Flow Through ◽  
Compute Time

Abstract. Depressions – inwardly draining regions – are common to many landscapes. When there is sufficient moisture, depressions take the form of lakes and wetlands; otherwise, they may be dry. Hydrological flow models used in geomorphology, hydrology, planetary science, soil and water conservation, and other fields often eliminate depressions through filling or breaching; however, this can produce unrealistic results. Models that retain depressions, on the other hand, are often undesirably expensive to run. In previous work we began to address this by developing a depression hierarchy data structure to capture the full topographic complexity of depressions in a region. Here, we extend this work by presenting the Fill–Spill–Merge algorithm that utilizes our depression hierarchy data structure to rapidly process and distribute runoff. Runoff fills depressions, which then overflow and spill into their neighbors. If both a depression and its neighbor fill, they merge. We provide a detailed explanation of the algorithm and results from two sample study areas. In these case studies, the algorithm runs 90–2600 times faster (with a reduction in compute time of 2000–63 000 times) than the commonly used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code with 97 % test coverage is available on GitHub and Zenodo.

scholarly journals Computing water flow through complex landscapes, Part 3: Fill-Spill-Merge: Flow routing in depression hierarchies

2020 ◽  
Author(s):  
Richard Barnes ◽  
Kerry L. Callaghan ◽  
Andrew D. Wickert
Keyword(s):  
Water Conservation ◽  
Source Code ◽  
Planetary Science ◽  
Topographic Complexity ◽  
Flow Models ◽  
Detailed Explanation ◽  
Jacobi Iteration ◽  
Flow Through ◽  
Soil And Water ◽  
Compute Time

Abstract. Depressions – inwardly-draining regions – are common to many landscapes. When there is sufficient moisture, depressions take the form of lakes and wetlands; otherwise, they may be dry. Hydrological flow models used in geomorphology, hydrology, planetary science, soil and water conservation, and other fields often eliminate depressions through filling or breaching; however, this can produce unrealistic results. Models that retain depressions, on the other hand, are often undesirably expensive to run. In previous work we began to address this by developing a depression hierarchy data structure to capture the full topographic complexity of depressions in a region. Here, we extend this work by presenting a Fill-Spill-Merge algorithm that utilizes our depression hierarchy to rapidly process and distribute runoff. Runoff fills depressions, which then overflow and spill into their neighbors. If both a depression and its neighbor fill, they merge. We provide a detailed explanation of the algorithm as well as results from two sample study areas. In these case studies, the algorithm runs 90–2600× faster (with a 2000–63 000× reduction in compute time) than the commonly-used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code is available on Github and Zenodo.

scholarly journals Computing water flow through complex landscapes, part 1: Incorporating depressions in flow routing using FlowFill

2019 ◽  
Author(s):  
Kerry L. Callaghan ◽  
Andrew D. Wickert
Keyword(s):  
Water Flow ◽  
Water Conservation ◽  
Planetary Science ◽  
Rapid Expansion ◽  
Hydrologic Connectivity ◽  
Drainage Network ◽  
Flow Routing ◽  
Data Errors ◽  
Hydrologic System ◽  
Flow Through

Abstract. Calculating flow routing across a landscape is a routine process in geomorphology, hydrology, planetary science, and soil and water conservation. Flow-routing calculations often require a preprocessing step to remove depressions from a DEM to create a flow-routing surface that can host a continuous, integrated drainage network. However, real landscapes contain natural depressions that trap water. These are an important part of the hydrologic system, and should be represented in flow-routing surfaces. Historically, depressions (or pits) in DEMs have been viewed as data errors, but the rapid expansion of high-resolution, high-precision DEM coverage increases the likelihood that depressions are real-world features. To address this longstanding problem of emerging significance, we developed FlowFill, an algorithm that routes a prescribed amount of runoff across the surface in order to flood depressions, but only if enough water is available. This mass-conserving approach typically floods smaller depressions and those in wet areas, integrating drainage across them, while permitting internal drainage and disruptions to hydrologic connectivity. We present results from two sample study areas to which we apply a range of uniform initial runoff depths and report the resulting filled and unfilled depressions, the drainage network structure, and the required compute time. Typical FlowFill calculations take minutes to perform and permit more realistic analyses of water flow across landscapes.

scholarly journals Computing water flow through complex landscapes – Part 1: Incorporating depressions in flow routing using FlowFill

2019 ◽  
Vol 7 (3) ◽  
pp. 737-753 ◽  
Author(s):  
Kerry L. Callaghan ◽  
Andrew D. Wickert
Keyword(s):  
Water Conservation ◽  
Planetary Science ◽  
Rapid Expansion ◽  
Hydrologic Connectivity ◽  
Drainage Network ◽  
Watershed Scale ◽  
Flow Routing ◽  
Data Errors ◽  
Hydrologic System ◽  
Flow Through

Abstract. Calculating flow routing across a landscape is a routine process in geomorphology, hydrology, planetary science, and soil and water conservation. Flow-routing calculations often require a preprocessing step to remove depressions from a DEM to create a “flow-routing surface” that can host a continuous, integrated drainage network. However, real landscapes contain natural depressions that trap water. These are an important part of the hydrologic system and should be represented in flow-routing surfaces. Historically, depressions (or “pits”) in DEMs have been viewed as data errors, but the rapid expansion of high-resolution, high-precision DEM coverage increases the likelihood that depressions are real-world features. To address this long-standing problem of emerging significance, we developed FlowFill, an algorithm that routes a prescribed amount of runoff across the surface in order to flood depressions if enough water is available. This mass-conserving approach typically floods smaller depressions and those in wet areas, integrating drainage across them, while permitting internal drainage and disruptions to hydrologic connectivity. We present results from two sample study areas to which we apply a range of uniform initial runoff depths and report the resulting filled and unfilled depressions, the drainage network structure, and the required compute time. For the reach- to watershed-scale examples that we ran, FlowFill compute times ranged from approximately 1 to 30 min, with compute times per cell of 0.0001 to 0.006 s.

scholarly journals Computing water flow through complex landscapes – Part 2: Finding hierarchies in depressions and morphological segmentations

2020 ◽  
Vol 8 (2) ◽  
pp. 431-445
Author(s):  
Richard Barnes ◽  
Kerry L. Callaghan ◽  
Andrew D. Wickert
Keyword(s):  
Water Flow ◽  
Hydrological Modeling ◽  
Dynamic Models ◽  
Terrain Analysis ◽  
Flow Paths ◽  
Topographic Complexity ◽  
Morphological Segmentation ◽  
Surface Water Flow ◽  
Digital Elevation ◽  
Flow Through

Abstract. Depressions – inwardly draining regions of digital elevation models – present difficulties for terrain analysis and hydrological modeling. Analogous “depressions” also arise in image processing and morphological segmentation, where they may represent noise, features of interest, or both. Here we provide a new data structure – the depression hierarchy – that captures the full topologic and topographic complexity of depressions in a region. We treat depressions as networks in a way that is analogous to surface-water flow paths, in which individual sub-depressions merge together to form meta-depressions in a process that continues until they begin to drain externally. This hierarchy can be used to selectively fill or breach depressions or to accelerate dynamic models of hydrological flow. Complete, well-commented, open-source code and correctness tests are available on GitHub and Zenodo.

scholarly journals A system of conservative regridding for ice/atmosphere coupling in a GCM

2013 ◽  
Vol 6 (4) ◽  
pp. 6493-6568 ◽  
Author(s):  
R. Fischer ◽  
S. Nowicki ◽  
M. Kelley ◽  
G. A. Schmidt
Keyword(s):  
Finite Element ◽  
General Circulation ◽  
Flow Model ◽  
Source Code ◽  
Circulation Model ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Flow Models ◽  
Ice Model

Abstract. The method of elevation classes has proven to be a useful way for a low-resolution general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields, for use in one-way studies coupling GCMs and ice flow models. Past uses of elevation classes have been a cause of non-conservation of mass and energy, caused by inconsistency in regridding schemes chosen to regrid to the atmosphere vs. downscaling to the ice model. This causes problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded, and five transformations between those grids required by a typical coupled GCM–ice flow model. This paper shows how each of those transformations may be achieved in a consistent, conservative manner. These transformations are implemented in GLINT2, a library used to couple GCMs with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.

scholarly journals Bedtk: finding interval overlap with implicit interval tree

2020 ◽  
Author(s):  
Heng Li ◽  
Jiazhen Rong
Keyword(s):  
Data Structure ◽  
Source Code ◽  
Interval Tree

Abstract Summary We present bedtk, a new toolkit for manipulating genomic intervals in the BED format. It supports sorting, merging, intersection, subtraction and the calculation of the breadth of coverage. Bedtk uses implicit interval tree, a data structure for fast interval overlap queries. It is several to tens of times faster than existing tools and tends to use less memory. Availability and implementation The source code is available at https://github.com/lh3/bedtk.

FRACTAL ANALYSES OF ANISOTROPIC FRACTURE SURFACES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 547-559 ◽  
Author(s):  
B.L. COX ◽  
J.S.Y. WANG
Keyword(s):  
Area Ratio ◽  
Affine Scaling ◽  
Rock Fractures ◽  
Flow Models ◽  
Anisotropic Fracture ◽  
Fractal Analyses ◽  
Dixie Valley ◽  
Flow Through ◽  
Self Similar ◽  
Simulated Flow

Natural surfaces of rock fractures often have anisotropic asperity distributions, especially for shear fractures or faults. The asperity distributions could be treated as self-affine fractals with directional dependent scaling in the plane of the rock surfaces. Different fractal analyses (divider, slit-island, variogram) are applied to surface distributions of asperity data (topography): (1) a granitic fracture from the Stripa mine in Sweden; (2) a faulted and geothermally altered fracture from Dixie Valley, Nevada, USA. The cutoff patterns (indicator maps) of the granitic fracture show a radial pattern, while those of the faulted fracture show a very anisotropic stretched pattern of shapes. Different cutoff patterns of the same surface generally yield the same fractal dimension with the slit-island technique. The slit-island technique assumes that the cut-off patterns are self-similar in the plane of the surface, with the perimeter versus area analyzed for the entire population of contours, regardless of aspect ratio. We measure the variance in the two coordinate directions as a function of perimeter/area ratio for the anisotropic fracture from Dixie Valley to determine a self-affine scaling ratio for the slit-island analysis. We compare this ratio with anisotropy ratios obtained from simulated flow models based on channeling of flow through the largest openings. The possible applications of fractal analyses to both the geometry and flow are evaluated.

scholarly journals MODEL OF COLLABORATIVE COURSES DEVELOPMENT IN DISTANCE LEARNING PLATFORMS

2015 ◽  
Vol 45 (1) ◽  
pp. 42
Author(s):  
Dmytro S. Morozov ◽  
Vitalii Ye. Zaitsev
Keyword(s):  
Data Structure ◽  
Distance Learning ◽  
Source Code ◽  
Research Paper ◽  
Educational Institutions ◽  
Basic Principles ◽  
Collaborative Development ◽  
Learning Platforms

The research paper outlines the problem of organization collaboration of users group on creation distance learning courses. The article contains analysis of the courses data structure. According to proposed structure the model of developer’s collaboration on creating distance learning courses based on basic principles of source code management was proposed. The article also provides result of research on necessary tools for collaborative development of courses in distance learning platforms. According to the requirements of flexibility and simplicity of access to system for any level educational institutions, technological decisions on granting permissions on performing basic operations on course elements and providing to user moderation’s privileges were proposed.

Experimental Study of Entrance Effects on Laminar Gas Flow Through Silicon Orifices

2005 ◽  
Author(s):  
Aaron J. Knobloch ◽  
Joell R. Hibshman ◽  
George Wu ◽  
Rich Saia
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Flow Area ◽  
Fully Developed Flow ◽  
Flow Rates ◽  
Flow Models ◽  
Entry Length ◽  
Orifice Flow ◽  
Measured Flow ◽  
Flow Through

This study summarizes a fundamental investigation of flow through an array of silicon micromachined rectangular slots. The purpose of the study is to evaluate the effect of entrance pressure, flow area, orifice thickness, slot length, and slot width of the orifice on flow rate. These orifices were fabricated using a simple frontside through wafer DRIE process on a 385 μm thick wafer and wafer bonding to create thicker orifices. The dies were then packaged as part of a TO8 can and flow tested. To complement the results of this experimental work, two simple flow models were developed to predict the effect of geometrical and entrance conditions on the flow rate. These models were based on macroscale assumptions that were not necessarily true in the case of thin orifices. One relationship was based on Pouiselle flow which assumes fully developed flow conditions. Calculation of the entry length required for fully developed flow indicate that in the low Reynolds Number regime (32-550) evaluated, the entry flow development requires 2-8 times the thickness of the thickest orifices used for this study. Therefore, calculations of orifice flow based on a Pouiselle model are an overestimate of the actual measured flow rates. Another model examined typical orifice relationships using head loss at the entrance and exit of the slots did not accurately capture the particular flow rates since it overestimated the expansion or constriction losses. A series of experiments where the pressure was varied between 75 and 1000 Pa were performed. A comparison of the Pouiselle flow solution with experimental results was made which showed that the Pouiselle flow model overpredicts the flow rates and more specifically, the effect of width on the flow rates. The results of these tests were used to develop a transfer function which describes the dependence of flow rate on orifice width, thickness, length, and inlet pressure.

Applicability of Choking Flow Models for Subcooled Flashing Flow Through Tube Cracks

2011 ◽  
Author(s):  
Brian Wolf ◽  
Shripad T. Revankar ◽  
Jovica R. Riznic
Keyword(s):  
Mechanistic Model ◽  
Channel Length ◽  
Two Phase ◽  
Experimental Conditions ◽  
Flow Rates ◽  
Flow Models ◽  
Model Predictions ◽  
Flow Through ◽  
The Difference ◽  
Non Equilibrium

Recently there is some database available on choking flow through cracks relevant to steam generator (SG) tubes to model the critical flow. These data are used in assessing the key choking flow models. Based on this assessment a mechanistic choking model is developed. The model is used to predict the choking flow rates for various experimental conditions for subcooled flashing flow through narrow slits with L/D varying from small values (∼5) to large values (100). Results are presented on the effects of thermal and mechanical non-equilibrium on the choking flow for small L/D channels. A mechanistic model was developed to model two-phase choking flow through slits. A comparison of model results to experimental data shows that the homogeneous equilibrium based models markedly under predict choking flow rates in such geometries. As subcooling increases, and channel length decreases the non-equilibrium effects play a greater role in the choking phenomenon, therefore the difference in model predictions and experimental results increases.

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